Signal-to-Noise Ratio (SNR). Detection of a signal from the background essentially corresponds to a binary classification problem. SNR is widely used to measure the potential detection performance before specifying the classifier [1]}. In particular, if we have two equiprobable classes \(\mathcal {C} = \lbrace -1,1\rbrace \)  and the features follows 1-d Gaussian distributions \(\mathbb {P}_{Y} = \mathcal {N}(\mu _{Y},\sigma ^2)\) , \(Y\in \mathcal {C}\) . The SNR \(\rho \)  defined as follows precisely characterizes the minimal Bayesian mis-classification error.
